IIs any attention being given to Conformal Cyclic Cosmology?

Conformal Cyclic Cosmology, or CCC, is a hypothesis put forward by Roger Penrose in the early 2000s. My understanding of physics is lacking so my explanation will not be that clear, but I will summarize it here.

Essentially, the existence of a previous spacetime, or "aeon," is postulated. This spacetime has a 3-manifold which bounds it at t=∞. This bounding 3-manifold is conformally re-scaled and glued to the past of our universe - so that the heat death of the previous universe is essentially the big bang of this one. Because of something to do with QFT (which I know basically nothing about), the photons of the previous aeon can carry over to this one and, as I understand, make up the CMB.

Penrose suggested that the concentric annuli of low temperature in the CMB act as preliminary evidence for this, as they could be caused by the gravitational waves of the last blackholes of the previous aeon colliding. I've come across a couple arXiv articles saying that these annuli are consistent with ΛCDM cosmology.

So it would seem that CCC is a no-go. However, Penrose and others recently published this paper on arXiv, which discusses anomalous points in the CMB sky and how they could be the result of the last blackholes of the previous aeon evaporating. In addition, according to the wikipedia, Penrose claims that CCC could explain the accelerating of the expansion of the universe without dark energy. Perhaps this is not so appealing since QFT predicts that there should be a much higher vacuum energy density than is actually observed.

Nonetheless, my question remains: is there anyone in the physics community doing research on what could further verify or falsify this model? And is anyone doing research on what it might imply for other areas of physics?

PS: I read on physics stackexchange that the original publication on CCC was "Causality, quantum theory and cosmology," published by Cambridge. I never found this online or in my univerity's library but I put in an inter-library request and got a pdf of it. I can email it to anyone who is interested and doesn't want to go through the trouble.

My understanding is that CCC actually needs dark energy to exist for it to work. Well a cosmological constant anyway. My impression is that there are a few other scientists that have published positive papers about CCC. So interest in it is not zero but its not large either. you can do a google scholar search and find a few papers.

If I understand Roger Penrose (highly unlikely but I digress) dark matter was present at the Big Bang but has been decaying away from the beginning. This might explain the change from a BB with low entropy to a CMB with high entropy. My question is this: if as Professor Penrose suggests, dark matter is decaying, wouldn't this be seen in a variation in galactic rotation curves over the course of history?

If I understand Roger Penrose (highly unlikely but I digress) dark matter was present at the Big Bang but has been decaying away from the beginning. This might explain the change from a BB with low entropy to a CMB with high entropy. My question is this: if as Professor Penrose suggests, dark matter is decaying, wouldn't this be seen in a variation in galactic rotation curves over the course of history?

Most dark matter models have dark matter slowly decaying and/or annihilating, but the rate is low enough that it doesn't have a significant impact on dark matter distributions. I don't think Penrose is assuming rapid decay, just eventual decay.

Most dark matter models have dark matter slowly decaying and/or annihilating, but the rate is low enough that it doesn't have a significant impact on dark matter distributions. I don't think Penrose is assuming rapid decay, just eventual decay.

Thanks for this help. Penrose speaks of a half life of around ten to the eleven years, so one order of magnitude greater than the age of the Universe.

Thanks for this help. Penrose speaks of a half life of around ten to the eleven years, so one order of magnitude greater than the age of the Universe.

The half-life could be much higher than that for dark matter and it shouldn't impact the model. Normal matter is expected to have a half life greater than ##10^{30}## years, so that will still be around. If Penrose is banking on normal matter also decaying, though, that's a problem.

I don't really know what the half-life of dark matter is in various models myself.